Divide √60.
2√5
To divide √60 by 2√5, you can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of 2√5, which is 2√5.
√60 / 2√5 = (√60 * 2√5) / (2√5 * 2√5)
= (2√300) / (4 * 5)
= (2 * 10√3) / 20
= 10√3 / 10
= √3
Therefore, √60 / 2√5 = √3.
To simplify the division of √60 by 2√5, we can use rationalization of the denominator.
Step 1: Express √60 and 2√5 as their simplest radical form.
√60 = √(2 x 2 x 3 x 5) = 2√15
2√5 remains the same.
Step 2: Rewrite the division expression.
√60 ÷ 2√5 = (2√15) ÷ (2√5)
Step 3: Rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is √5.
(2√15) ÷ (2√5) x (√5/√5) = (2√15 x √5) ÷ (2√5 x √5) = (2√(15 x 5)) ÷ (2 x 5) = 2√75 ÷ 10
Step 4: Simplify the expression further.
2√75 ÷ 10 = (2 x 5 x √3) ÷ 10 = (10√3) ÷ 10 = √3
Therefore, √60 ÷ 2√5 simplifies to √3.
To divide √60 by 2√5, we can use rationalizing the denominator technique.
Step 1: Start with the expression √60.
Step 2: Simplify the expression by factoring the number under the square root sign. The prime factorization of 60 is 2 * 2 * 3 * 5. Therefore, we can rewrite √60 as √(2 * 2 * 3 * 5).
Step 3: Simplify the expression further by taking out any perfect square factors from under the square root. In this case, we can take out 2 * 2 = 4 since it is a perfect square. Therefore, √(2 * 2 * 3 * 5) can be written as 2 * √(3 * 5).
Step 4: Rewrite the expression by dividing the numbers outside the square root sign and multiplying the numbers inside. So, √60 becomes 2√(3 * 5).
Step 5: Finally, divide 2√(3 * 5) by 2√5. Since the numbers inside the square root signs are the same (3 * 5 = 15), we can eliminate them. Therefore, the final answer is 2.
So, √60 divided by 2√5 is equal to 2.